Bill: is the largest play, a reverse sente which gains 2 1/4 points. gains 2 points. Then - is a 1 1/4 point sente. At this point only 1 point (miai value) and smaller moves are left. (The temperature is 1.) But is a mistake, because it allows White to get the last play (tedomari) at the 2 level.
Without reading out the rest we can estimate the difference. Black gains 2 1/4 points and then loses 2 points, for a net gain of 1/4 point. The sente, - , gains nothing on average. Now having sente is worth 1/2 point, on average (half the temperature). So we can estimate Black's gain as 3/4 point.
OTOH, in the game Black played the 2 point gote (miai value) at a, allowing White to play the 2 1/4 point sente before the temperature dropped to 1. Black gained 2 points and lost an estimated 1/2 point, for an estimated gain of 1 1/2 points. That's 3/4 point better for Black, on average. And, in fact, Black did 1 point better in the game than by optimal play after in this diagram.
Bill: is the proper technique.
Bill: Black gets the last one point play with .
Black has captured 7 White stones.
White has captured 6 Black stones.
Black has gained 11/12 of a point in this line of play: 1/4 point before the drop to the 1 level, plus 1 point for getting the last 1 point play, minus 5/6 on the bottom side, plus 1/2 on the right side. In the game Black gained 1 11/12 points: 2 points at the 2 level, minus 5/6 on the bottom side, plus 3/4 on the right side, to win by 1 point.